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arXiv · 2512.20169

Learning to Reason in LLMs by Expectation Maximization

Junghyun Lee·Branislav Kveton·Anup Rao·Subhojyoti Mukherjee·Ryan A. Rossi·Sunav Choudhary·Alexa Siu
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Abstract

Large language models (LLMs) solve reasoning problems by first generating a rationale and then answering. We formalize reasoning as a latent variable model and derive a reward-based filtered expectation-maximization (FEM) objective for learning to reason. This view connects EM and modern reward-based optimization, and shows that the main challenge lies in designing a sampling distribution of rationales that justify correct answers. We instantiate and compare three sampling schemes: rejection sampling with a budget, self-taught reasoner (STaR), and prompt posterior sampling (PPS), which only keeps the rationalization stage of STaR that conditions on the correct answer in the prompt. We experiment with LLM-as-a-judge calibration and summarization from feedback tasks, where conditioning on the correct answer provides a strong guidance for generating rationales. Our experiments show the efficacy of PPS over other sampling schemes, and that the sampling scheme can have a significant impact on performance.

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Junghyun Lee, Branislav Kveton, Anup Rao, Subhojyoti Mukherjee, Ryan A. Rossi, Sunav Choudhary, Alexa Siu. 2025-12-23. Learning to Reason in LLMs by Expectation Maximization. https://arxiv.org/abs/2512.20169

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